Voltage amplifiers are provided in various analog signal processing circuits. FIG. 1 is a circuit diagram of a conventional variable gain amplifier 100r. As shown in FIG. 1, the variable gain amplifier 100r is an inverting amplifier that includes an operational amplifier 10, an input resistor Rin and a feedback resistor Rfb. The input resistor Rin is interposed between an inverted input terminal of the operational amplifier 10 and a first input terminal Pi1. A non-inverted terminal of the operational amplifier 10 is connected to a second input terminal Pi2 and an output terminal of the operation amplifier 10 is connected to an overall output terminal Po of the variable gain amplifier 100r. The feedback resistor Rfb is interposed between the output terminal and the inverted input terminal of the operational amplifier 10.
A gain Av of the variable gain amplifier 100r is given by the following Equation 1.Av=Rfb/Rin  [Equation 1]
The gain Av, which is inversely proportional to the input resistor Rin and is proportional to the feedback resistor Rfb, may be controlled by varying at least one of Rfb and Rin. Varying the value of the feedback resistor Rfb is desired due to its controllability and design flexibility.
The feedback resistor Rfb includes a plurality of resistors R10 to R14 connected in series, and switches SW1 to SW4 connected in parallel to the respective resistors R11 to R14. When all of the switches SW1 to SW4 are switched OFF, the gain Av of the variable gain amplifier 100r takes the maximum value which is equal to (R10+R11+R12+R13+R14)/Rin. When an i-th switch SWi is switched ON, a corresponding resistor R1i is bypassed to decrease the resistance of the feedback resistor Rfb leading to a decrease in the value of the gain Av.
The inventor has reviewed the variable gain amplifier 100r and was aware of the following problem. On-resistance of an ideal switch is zero. However, an actual switch using a MOSFET (Metal Oxide Semiconductor Field Effect Transistor) has an on-resistance. Accordingly, when the i-th switch SWi is switched on, the total resistance value of the feedback resistor Rfb is affected by on-resistance Roni of the switch SWi. Specifically, each switching state and the gain Av of the variable gain amplifier 100r have the following relationships.
SW1 to SW4 all OFFAv=(R10+R11+R12+R13+R14)/Rin  (2a)
SW1 ON and SW2 to SW4 OFFAv=(Ron1+R12+R13+R14)/Rin  (2b)
SW1 and SW2 ON and SW3 and SW4 OFFAv=(Ron1+Ron2+R13+R14)/Rin  (2c)
SW1 to SW3 ON and SW4 OFFAv=(Ron1+Ron2+Ron3+R14)/Rin  (2d)
SW1 to SW4 all ONAv=(Ron1+Ron2+Ron3+Ron4)/Rin  (2e)
In other words, in the variable gain amplifier 100r of FIG. 1, the on-resistance of the switches causes an unavoidable gain error.